電子學手冊/元件/電容器/雙埠連線

分壓器

上圖所示的兩個電阻串聯的電路

$I={\frac {V}{R_{2}+R_{1}}}$

$V_{o}=IR_{2}=V{\frac {R_{2}}{R_{2}+R_{1}}}$

${\frac {V_{o}}{V_{i}}}={\frac {R_{2}}{R_{2}+R_{1}}}$

T 型電路

如果 R₂ 上的電壓為 V

$V=V_{2}{\frac {R_{1}}{R_{1}+R_{3}}}=V_{1}{\frac {R_{1}}{R_{2}+R_{1}}}$

${\frac {V_{1}}{V_{2}}}={\frac {R_{1}+R_{2}}{R_{1}+R_{3}}}$

π 型電路

一個電路，其中三個電阻以 π 形連線。R₁ 在輸入端，R₃ 在輸出端

I_R1 = I_R2 + I_R3

${\frac {v_{i}}{R_{1}}}={\frac {v_{i}-v_{o}}{R_{2}}}+{\frac {v_{o}}{R_{3}}}$

${\frac {v_{i}}{v_{o}}}=({\frac {R_{3}}{R_{1}}})({\frac {R_{2}-R_{1}}{R_{2}-R_{3}}})$

${\frac {v_{o}}{v_{i}}}=({\frac {R_{3}}{R_{1}}})({\frac {R_{2}-R_{1}}{R_{2}-R_{3}}})$

串聯並聯電路

$R_{EQ}=(R_{1}\|R_{2})+R_{3}={R_{1}R_{2} \over R_{1}+R_{2}}+R_{3}$

轉換

Δ-Y 轉換

$R_{1}={\frac {R_{\mathrm {a} }R_{\mathrm {b} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}$

<math>R_2 = \frac{R_\mathrm{a} R_\mathrm{c}}{R_\mathrm{a} + R_\mathrm{b} + R_\mathrm{c}}

$R_{3}={\frac {R_{\mathrm {c} }R_{\mathrm {a} }}{R_{\mathrm {a} }+R_{\mathrm {b} }+R_{\mathrm {c} }}}$

Y-Δ 轉換

$R_{\mathrm {a} }={\frac {R_{1}R_{2}+R_{2}R_{3}+R_{3}R_{1}}{R_{2}}}$

$R_{\mathrm {b} }={\frac {R_{1}R_{2}+R_{2}R_{3}+R_{3}R_{1}}{R_{3}}}$

$R_{\mathrm {c} }={\frac {R_{1}R_{2}+R_{2}R_{3}+R_{3}R_{1}}{R_{1}}}$